Under slow fading conditions, the channel gain of an Aditive White Gaussian Noise (AWGN) channel, which is generally modeled as a wide-sense stationary (WSS) random process \(\alpha (t,\omega )\) , varies slowly with respect to the time duration of a codeword. In these situations, the value of the channel gain during the transmission of a codeword can be considered to be approximately constant and given by a realization of the random variable \(\alpha (\omega )\) . Therefore, the block fading channel can be reduced to an AWGN channel where the received signal-to-noise ratio is a random variable \(|\alpha (\omega )|^2 \mathrm {SNR}\) . Consequently, the channel capacity also becomes the random variable \(C(\omega ) = \log _2(1 + |\alpha (\omega )|^2 \mathrm {SNR})\)  with bits per channel use serving as the measuring units.
Note that by the Shannon channel coding theorem, given an encoding rate \(R\)  bits per channel use, reliable communication will be possible if the realization of the channel capacity \(C(\omega )\)  is larger than \(R\) . On the other hand, when \(C<R\)  communication with low probability of error is not possible. The probability that communications fail when transmitting a codeword with rate \(R\)  is called outage probability and is given by [1]}
\(\begin{split}p_{\mathrm {out}}(R,\mathrm {SNR}) &= \mathrm {P}(\lbrace \omega \in \Omega : C(\omega ) < R\rbrace ) \\ &= P(\lbrace \omega \in \Omega : \log _2(1+|\alpha (\omega )|^2 \mathrm {SNR}) < R\rbrace ).\end{split}\) 
